one requires
new fermions, also known as anomalons,
which cancel the anomalies of the new \({\rm U}(1)_X\)  factor,
also
in combination
with the electroweak gauge group.
Note that Eq. (REF ) is the most general linear combination of abelian global symmetries of the SM that
can be gauged,
under the assumption that all SM Yukawa operators are allowed in the quark sector at the renormalizable level.
Barring the cases of \(B/3 - L_i\)  and linear combinations thereof,
the anomalons
need to be charged under the electroweak gauge group (henceforth indicated more precisely as electroweak anomalons).This is not the case if
some of the quark Yukawa operators arise at the non-renormalizable level,
as e.g. discussed recently in Ref. [1]}.
In the latter case, in order to
evade detection at high-energy particle colliders,
the new fermions need to be heavier than the electroweak scale.
Consequently, their effects on the physics of the light vector boson associated with the \({\rm U}(1)_X\)  gauge symmetry,
here denoted as \(\mathcal {X}\) ,
can be described within
an effective field theory (EFT) approch. In particular,
after integrating out the new heavy fermions at one loop,
one generates
dimension-4 Wess-Zumino (WZ)
terms, schematically
of the form \(\mathcal {X}(W \partial W + WWW)\)  and \(\mathcal {X}B \partial B\) 
(with \(W\)  and \(B\)  denoting \({\rm SU}(2)_L\)  and \({\rm U}(1)_Y\)  gauge bosons).
These
contact interactions have the role of compensating,
in the EFT
without electroweak anomalons,
the
anomalous shift of the effective action
due to the anomalous SM fermion current coupled to \(\mathcal {X}\) 
(see e.g. [2]}, [3]}, [4]}, [5]}).
